ocaml: phase 5.1 levenshtein.ml baseline (no-memo edit distance, sum=11)

Recursive Levenshtein edit distance with no memoization (the test
strings are short enough for the exponential-without-memo version to
fit in <2 minutes on contended hosts). Sums distances for five short
pairs:

  ('abc','abx') + ('ab','ba') + ('abc','axyc') + ('','abcd') + ('ab','')
   = 1 + 2 + 2 + 4 + 2 = 11

Exercises:
  * curried four-arg recursion
  * s.[i] equality test (char comparison)
  * min nested twice for the three-way recurrence
  * mixed empty-string base cases

lib/ocaml/baseline/expected.json

@@ -11,6 +11,7 @@
   "fizzbuzz.ml": 57,
   "list_ops.ml": 30,
   "lambda_calc.ml": 7,
+  "levenshtein.ml": 11,
   "memo_fib.ml": 75025,
   "module_use.ml": 3,
   "mutable_record.ml": 10,

lib/ocaml/baseline/levenshtein.ml

@@ -0,0 +1,18 @@
+let rec lev s1 s2 i j =
+  if i = 0 then j
+  else if j = 0 then i
+  else if s1.[i - 1] = s2.[j - 1] then
+    lev s1 s2 (i - 1) (j - 1)
+  else
+    1 + min (lev s1 s2 (i - 1) j)
+            (min (lev s1 s2 i (j - 1)) (lev s1 s2 (i - 1) (j - 1)))
+
+let dist s1 s2 = lev s1 s2 (String.length s1) (String.length s2)
+
+;;
+
+dist "abc" "abx"
++ dist "ab" "ba"
++ dist "abc" "axyc"
++ dist "" "abcd"
++ dist "ab" ""

plans/ocaml-on-sx.md

@@ -407,6 +407,12 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 5.1 — levenshtein.ml baseline (recursive edit
+  distance, no memo). Sums distances for five short pairs:
+  ("abc","abx")=1 + ("ab","ba")=2 + ("abc","axyc")=2 +
+  ("","abcd")=4 + ("ab","")=2 = 11. Exercises curried four-arg
+  recursion + s.[i] equality test + min nested twice + mixed empty
+  string base cases.
 - 2026-05-09 Phase 5.1 — caesar.ml baseline (ROT13 with String.init +
   s.[i] + Char.code/chr). Side-quests:
   (1) top-level `let r = expr in body` is now treated as an expression